Step 1. Formulation of the problem
We know that
The total number of tickets sold = 400
The cost of a ticket for adults = Rs. 20
The cost of the ticket for student = Rs. 10
and the total proceedings were = Rs. 6000
Mathematical formulation : Let the number of adults who visited the fair be x
∴ number of students visited = (400 - x)
Total amount received from adults = Rs. 20x
Total amount received from students = Rs. 10(400 - x)
Total amount collected = Rs. 6000
∴ the model (relation) is 20x + 10(400 - x) = 6000
Step 2. Finding the solutions
20x + 4000 - 10x = 6000
=> 10x + 4000 = 6000
=> 10x = 2000
=> x = 200
Step 3. Interpretation of the solution
We assumed that the number of adults who visited the fair was x
∴ 200 adults visited the fair.
Step 4. Validation of the result
No. of adults who visited the fair = 200
No. of students who visited the fair = (400 - 200) = 200
∴ Total receipts = Rs (20 × 200) + Rs. (10 × 200)
= Rs. 4000 + Rs. 2000
= Rs. 6000
Thus, the total collection from 200 adults and 200 students is Rs. 6000.
